1 gek1536 computation & machine, ancient to modern

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GEK1536Computation & Machine, Ancient to Modern

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Computation & Machine: Ancient to Modern

By Prof Wang Jian-Shengcscwjs@nus.edu.sgDepartment of Physics

GEK1536

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Course Information Course Website

http://web.cz3.nus.edu.sg/~wangjs/GEM/gem.html (see also IVLE)

Class ScheduleLectures (LT26): Wed 4:00-6:00pmTutorials (S16 #03-03): once every week, slots: Mon 9-10, Tue 9-10, Wed 10-11, 11-12, Thu 2-3, 3-4, Fri 12-1, 1-2.Download your tutorial problem set at least one week ahead of time.

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Assessment

40% final (closed book)

40% tutorial/homework (once every week)

20% Midterm (1 hour on week 8)

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Aim, Objective, Syllabus

Numbers and their representations Historic perspective of computation Primitive computing tools (abacus,

sliding rule, etc) Development of digital computer and

machine language Future computing machines

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Outline of Topics Oh, So Mysterious

Egyptian Mathematics

Mesopotamia Here We Come

These Incredible Greeks

Counting Boards Quest of

Babbage and his Computing Engine

Turing Machines Zeros and Ones The Digital Age Machine Instructions

& Computer Languages

Quantum Computing

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Reference Books

“The Saga of Mathematics, A brief history”, Lewinter & Widulski (Prentice Hall, 2002)

“From One to Zero, a universal history of numbers”, Ifrah (Viking, 1985)

“Computing before Computers”, Aspray (Iowa State, 1990)

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Egyptian Mathematics

The knob of King Narmer’s club, circa 3000 BC.

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Egyptian Numerals

Egyptian number system is additive.

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Mesopotamia Civilization

Above: Babylonian sexagesimal (base 60) number. It is the first positional number system.

Left: Oldest cuneiform writing by Sumerian.

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Roman Numerals

I 1

II 2

III 3

IV 4

V 5

VI 6

VII 7

VIII 8

IX 9

X 10

L 50

C 100

D 500

M 1000

MMMDCCCLXXVIII 3878

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Abaci

Boethius (Hindu-Arabic) vs Pythagoras (counting board)

Chinese Abacus

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Logarithm and Slide Rule

If ay=x, then y = logax

log (u v) = log (u) + log(v)

John Napier of Scotland developed the concept of logarithm around AD 1600.

Slide rule based on the property of logarithm was invented in the late 1700s.

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Charles Babbage

Difference Engine, around year 1871. A machine that can calculate a table of quadratic functions such as T(x)=x2+x+41.

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Vacuum Tubes & Transistors

Earliest generation digital computers are made of vacuum tubes. Transistors are invented in the late 1940s.

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Start of Digital Computer, the ENIAC

Built in 1943-45 at the Moore School of the University of Pennsylvania for the War effort by John Mauchly and J. Presper Eckert, but not delivered to the Army until just after the end of the war, the Electronic Numerical Integrator And Computer (ENIAC) was the first general-purpose electronic digital computer.

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Programming the Computer

Programming the ENIAC is by wiring the cables and flipping the switches.

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Modern Computer and Programming

#include <stdio.h>

main()

{

int a, b, c;

printf(“Hello\n”);

a=1; b = 2;

c = a + b;

printf(“c=%d”, c);

return;

}A modern Pentium PC from Dell.

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Computer ArchitectureA Pentium 4 CPU

add $8, $9, $10

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Turing Machine

A Turing Machine includes a head moving on a tape, an internal state, and instructions. Any computer can be made to be equivalent to a Turing machine.

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Binary Number System for Digital Computer

0000 0000 0 0100 0001 A

0000 0001 1 0100 0010 B

0000 0010 2 0100 0011 C

0000 0011 3 0100 0100 D

0000 0100 4 0100 0101 E

0000 0101 5 0100 0110 F

0000 0110 6 0100 0111 G

0000 0111 7 0100 1000 H

0000 1000 8 0100 1001 I

0011 1110 1000 0000 0000 0000 0000 0000 0.25

inte

ger

chara

cter

float-point number

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Quantum Computing

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Reminder

Load your lecture notes at course website (http://web.cz3.nus.edu.sg/~wangjs/GEM/gem.html)

Sign up for your tutorials (Starting Friday)

Print your tutorial sheets